$ x_{k-1} = x_k + V_k*Max(Min([\frac{\sigma_{k+1}}{\sigma_{k}}(\frac{x_{k}-x_{k+1}}{V_{k+1}})^\gamma + \frac{\lambda}{(\gamma+1)\eta}*\frac{\nu_{k+1}^2}{\sigma_{k}}]^\frac{1}{\gamma}, MAXPOV), MINPOV) $
$ Objective = \frac{\eta*\sum_{k=1}^{N}\sigma_k\frac{(x_{k-1}-x_k)^{\gamma+1}}{V_{k}^\gamma}}{\sqrt{mean(x)}}+\frac{\lambda*\sum_{k=1}^{N}x_{k-1}^2\nu_k^2}{orderqty^2} $
I have this recursive formula for a finite sequence. $X_N$ and $X_{N-1}$ is known. All those V, sigma, eta, gamma are known. So I would like to deduce the whole sequence $x_1$, $x_2$,..., $x_{N-2}$(around 200 numbers). But the square root component is really giving me a headache because it depends on the whole sequence.
Is it solvable? Please can anyone shed some light on how to calculate the whole sequence? Or how to simplify the calculation?